Painlevé I, coverings of the sphere and Belyi functions

DOI10.1007/s00365-013-9185-3zbMath1322.34100arXiv1207.4361OpenAlexW2010341774MaRDI QIDQ485289

Davide Masoero

Publication date: 9 January 2015

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4361

zbMATH Keywords

Painlevé equationsanharmonic oscillatorsBelyi functionsapproximation of meromorphic functions by rational functionsDubrovin's conjecture on tritronquee solution

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Arithmetic aspects of dessins d'enfants, Bely? theory (11G32)

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Dynamics of singular complex analytic vector fields with essential singularities II ⋮ Poles of Painlevé IV rationals and their distribution ⋮ Roots of generalised Hermite polynomials when both parameters are large ⋮ Modular forms, Schwarzian conditions, and symmetries of differential equations in physics

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